Slope of a Line
Slope of a line is a fundamental Grade 7 math skill from Yoshiwara Intermediate Algebra measuring the steepness and direction of a line. Slope m = (y2-y1)/(x2-x1) represents the rise over run between any two points on the line.
Key Concepts
Property The slope of a line is a rate of change that measures the steepness of the line.
It is defined as the ratio of the change in the y coordinate to the change in the x coordinate. In symbols: $$m = \frac{\Delta y}{\Delta x} = \frac{\text{change in } y\text{ coordinate}}{\text{change in } x\text{ coordinate}}$$ where $\Delta x$ is positive if we move right and negative if we move left, and $\Delta y$ is positive if we move up and negative if we move down.
Examples A line passes through the points $(3, 5)$ and $(7, 13)$. Its slope is $m = \frac{13 5}{7 3} = \frac{8}{4} = 2$. For a line containing points $( 2, 9)$ and $(4, 6)$, the slope is $m = \frac{6 9}{4 ( 2)} = \frac{ 3}{6} = \frac{1}{2}$. The slope of a line passing through $(100, 50)$ and $(120, 40)$ is $m = \frac{40 50}{120 100} = \frac{ 10}{20} = 0.5$.
Common Questions
What is the slope of a line?
Slope m = (y2-y1)/(x2-x1) is the ratio of vertical change (rise) to horizontal change (run) between two points on a line.
What does a positive slope mean?
A positive slope means the line rises from left to right. A negative slope means it falls from left to right.
How do you find the slope from a graph?
Choose two clear points on the line, count the rise (vertical change) and run (horizontal change) between them, then compute rise/run.
What is the slope of a line through (1,3) and (4,9)?
m = (9-3)/(4-1) = 6/3 = 2. The line rises 2 units for every 1 unit moved right.